A Way to Complete General Relativity
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The current study presents the remodeling of General Relativity (GR) where gravitational effects are explained by phase dynamics in a two-dimensional time space instead of curvature of spacetime. It is based on previously modified formulation of special relativity, where motion of particles is linked to a unitary constraint of temporal velocity, and the relativistic effects have time dependence of an internal time phase. The study generalizes the principle of equivalence by supposing that gravitational interactions only act on the phase degrees of freedom of time and space but the geometry of spacetime is still flat. In this context, the study derives the principles of invariant action of phase evolution as well as the equations of motion of massive particles and photons in the time manifold. Additionally, the research obtained explicit solutions of inertial motion, uniform acceleration, and spherically-symmetric gravitational fields. The theory in the weak-field regime regenerates Newtonian gravity and standard results of GR. Meanwhile, the formulation is fundamentally different to Einstein’s gravity in that the curvature of spacetime is not a dynamical variable. This leads to the fact that there are no curvature singularities, and event horizons are well-defined. The findings indicate that relativistic gravitation can be systematically developed in phase evolution instead of spacetime geometry. This offers an alternative theoretical framework with a structure that can be extended appropriately in the future
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